plz help.................

For inequality –3(2x – 5) < 5(2 – x)  the correct option is (–6x + 15 < 10 – 5x).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, indicating that they are not equal.

To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify the expression first.

Starting with the left-hand side, we can distribute the –3 to get:

–3(2x – 5) = –6x + 15

For the right-hand side, we can distribute the 5 to get:

5(2 – x) = 10 – 5x

Substituting these back into the original inequality, we get:

–6x + 15 < 10 – 5x

To solve for x, we can first move all the x terms to one side by adding 5x to both sides:

–x + 15 < 10

Then, we can move the constant term to the other side by subtracting 15 from both sides:

–x < –5

Finally, we can divide both sides by –1 (remembering to flip the inequality sign since we're dividing by a negative number) to get:

x > 5

So the first correct representation of the inequality is x > 5.

To get the second correct representation, we can also start with the inequality –6x + 15 < 10 – 5x, and move all the x terms to one side:

–6x + 5x < 10 – 15

So second option (–6x + 15 < 10 – 5x) are correct representations of the inequality.

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18. Perimeter of rectangle = 2(l + b)

l = 16m

b = 12m

Perimeter of rectangular park = 2 (12 + 16)

= 24 + 32

= 56m

Perimeter of square park = 56m

(given that, perimeter of rectangular and square park are equal)

Perimeter of square = 4a

4a = 56

a = 56/4

a = 14m

Area of square park = a²

= 14²

= 196m²

Answer: Evaluate the findings to compare to his hypothesis

Step-by-step explanation: Since the biologist already has the findings and has a hypothesis, he now has to compare both of them together.

The population when t=10 is approximately 281943.6.

This problem can be modeled by the following differential equation:

dp/dt = -k*p, where k is a constant of proportionality.

The general solution to this differential equation is:

p(t) = \(Ce^{(-k*t)}\), where C is a constant of integration.

We can use the given initial conditions to find the values of C and k.

p(2) = 400000 = \(Ce^{(-2k)}\)

p(4) = 350000 = \(Ce^{(-4k)}\)

Dividing these equations, we get:

400000/350000 = \(e^{(2k)}\)

ln(400000/350000) = 2k

k = ln(400000/350000) / 2

k ≈ 0.0436

Substituting this value of k into one of the initial conditions, we get:

400000 = \(Ce^{(-2*0.0436)}\)

C ≈ 496277.4

Therefore, the population function is:

p(t) = 496277.4 \(e^{(-0.0436*t)}\)

To find the population when t=10, we can substitute t=10 into this function:

p(10) = 496277.4\(e^{(-0.0436*10)}\) ≈ 281943.6

Therefore, the population when t=10 is approximately 281943.6.

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The solution to the equation 91 = 29^x is approximately x ≈ 1.08.

To solve for x in equation 91 = 29^x, we need to isolate the variable x. Here's the step-by-step process:

Add 150 to both sides of the equation to get rid of the constant term:

91 + 150 = 29^x + 150

Simplify the equation:

241 = 29^x + 150

Subtract 150 from both sides:

241 - 150 = 29^x

Simplify further:

91 = 29^x

Now, we can solve for x by taking the logarithm of both sides of the equation with base 29. Using the logarithm property log_b(a^c) = c * log_b(a), we have:

log_29(91) = x

Using a calculator or logarithm table, we can find that log_29(91) ≈ 1.08.

Therefore, the solution to the equation 91 = 29^x is approximately x ≈ 1.08.

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Sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.

" Sale price is defined as the amount on which something is sold out."

Formula used

Sale price = Cost price - Discount amount

According to the question,

Cost price of the crate of pears = $50

Discount  on sale price = 10%

Discount amount = 10% of $50

                             \(=\frac{10}{100}(50) \\\\= \$5\)

Substitute the value in the formula of sale price we get,

Sale price = \(\$ ( 50 - 5)\)

                 = $ 45

Hence, sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.

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The ordered pair for the given solution set should be (-1, 6) when the graph solution set for the given inequality function is involved.

What is inequality function?

Since an inequality is merely a particular kind of relation, we can graph it just like we would any other relation. When dealing with inequalities, the trick is to shade large portions of the graph rather than using lines to connect the dots. But you could use some cover.

The given inequality function be like

y > 1 ÷ 3x + 4

The ordered pair refer to the solution set that provided by plotting the graph of the inequality, that expressed the inequality where an equation, plotting the graph along with a solid line, and shading the sides should be above the line of the graph to show the greater than or equal to sign.

Hence, the ordered pair for the given solution set should be (-1,6).

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The expected market price for the bond is $2,250.63.

To calculate the expected market price for the bond, we can use the present value formula in Excel.

Assuming that the yield to maturity is an annual rate, we can calculate the expected market price using the following formula in Excel:

=PV(rate, nper, pmt, fv)

where:

rate: Yield to maturity per period (10%)

nper: Number of periods (24)

pmt: Coupon payment per period (0, since it's a zero-coupon bond)

fv: Face value (par value) of the bond ($10,000)

Here's how you can enter the formula and calculate the expected market price in Excel:

1. In cell A1, enter the label "Yield to Maturity".

2. In cell A2, enter the yield to maturity as a decimal value (0.10).

3. In cell B1, enter the label "Number of Periods".

4. In cell B2, enter the number of periods (24).

5. In cell C1, enter the label "Coupon Payment".

6. In cell C2, enter the coupon payment amount (0, since it's a zero-coupon bond).

7. In cell D1, enter the label "Face Value".

8. In cell D2, enter the face value of the bond ($10,000).

9. In cell E1, enter the label "Expected Market Price".

10. In cell E2, enter the following formula: =PV\(($A$2, $B$2, $C$2, $D$2).\)

Excel will calculate the expected market price based on the formula. The result will be displayed in cell E2.

The correct answer is: $2,250.63 (Option D).

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Answer:

between quadrant 2 and 3

Step-by-step explanation:

Answer:

I.4

ii.13

Step-by-step explanation:

....ur welcome........

Answer:

94 cm²

Step-by-step explanation:

= 2 × (5×3 + 5×4 + 3×4)

= 2 × (15 + 20 + 12)

= 2 × 47

= 94 cm²

Answer:

C

Step-by-step explanation:

Dialation because when a shape is made bigger it cannot be mapped back on its self correctly

The final result is: 30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8

The box method, also known as the FOIL method, is a way of multiplying two polynomials by using the distributive property.

Given the expression (5x - 1)(6x^2 + 3x + 8), we can use the box method to multiply the terms as follows:

Therefore., the final result is:

30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8

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The new number in the sequence is found to be 7.

In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.

A sequence can be arranged in either ascending or descending order.

There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.

According to the question, the sequence follows the pattern:

Next number=2(Previous number)-2

On substituting the values,

48=2(Previous number)-2

50=2(Previous number)

Previous number=\(\frac{50}{2}\)=25

New number=sum of digits of the previous number in the sequence

                     =2+5

                     =7

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Answer:

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point

Answer:

answer is c!

because it's domain is -7!!

Answer: The parabola is wider than the parent function

Step-by-step explanation:

If "a" is a fraction less than one, then the parabola becomes wider.

See graph (attached)

An Investment of $10,000 yields 8% interest compounded quarterly.  The accumulated capital after 6 months is $10,404. The accumulated capital after 5 years is $14.859.47

From the information given;

a. we are to determine the amount of the accumulated capital after 6 months.

Now, using the formula for calculating the amount value of the accumulated capital:

\(\mathbf{A = P(1 + \dfrac{r}{n})^{nt}}\)

\(\mathbf{A = 10000(1 + \dfrac{0.08\times 1}{4})^{4 \times \frac{1}{2}}}\)

\(\mathbf{A = 10000(1.02)^2}}\)

A = $10,404

b. we are to determine the amount of the accumulated capital after 5 years

\(\mathbf{A = P(1 + \dfrac{r}{n})^{nt}}\)

\(\mathbf{A = 10000(1 + \dfrac{0.08\times 1}{4})^{4 \times 5}}\)

\(\mathbf{A = 10000(1.02)^20}}\)

A = $14859.47

Therefore, we can conclude that the accumulated capital after 6 months is $10,404 and the accumulated capital after 5 years is $14859.47

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Yes, it is possible to have a function f defined on [2, 3] that meets the given conditions. To satisfy the condition of not being continuous on [2, 3], we can create a function with a removable discontinuity at a specific point.

One way to achieve this is by defining f(x) as a piecewise function. We can let f(x) be equal to a constant value c for x in [2, a) and [a, 3], where a is a value between 2 and 3. This will create a hole in the graph of the function at x = a, resulting in a removable discontinuity.

To ensure that f takes on both a maximum and minimum value, we can choose different constant values for f(x) in the intervals [2, a) and [a, 3]. For example, we can let f(x) be a high value like 100 in [2, a) and a low value like -100 in [a, 3]. This way, f(x) will have a maximum value of 100 and a minimum value of -100.

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Answer:

29

Step-by-step explanation:

g=6 g+23

substitute g=6 into the equation

(6)+23

29

29 is your answer

Answer:

A

Step-by-step explanation:

a function must not repeat the input and B repeats 9 twice and you get two different outputs.

Answer:

A

Step-by-step explanation:

Because a is a functioning pair.

The alternative that proportionates the greatest quality of the product R is alternative 3. This can be justified mathematically.

In order to determine the greatest quality of the product R, we need to consider the stoichiometry of the reaction and the conditions of the reactors. The fact that the reaction is elemental in the liquid state means that the reaction is highly dependent on the reactant concentrations and the residence time of the reactants in the reactors.

By using plug flow reactors, we ensure that the reactants flow through the reactors without any mixing or backflow. This allows for better control over the reaction conditions and minimizes side reactions.

Alternative 3, which consists of two reactors, will provide a larger total volume for the reaction compared to the other alternatives. This means that the reactants will have a longer residence time in the reactors, allowing for a higher conversion of reactants to product R.

Additionally, the larger volume in alternative 3 will allow for better temperature and concentration control, leading to a higher quality product R.

Therefore, alternative 3 proportionates the greatest quality of the product R based on the stoichiometry of the reaction and the use of plug flow reactors.

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The largest figure that Ash can built with 61 toothpicks is of:

A composition of 12 hexagons.

The number of toothpicks needed is modeled with a linear function, defined as follows:

y = mx + b.

The coefficients of the function are given as follows:

The number of toothpicks in each figure is represented by the following sequence:

(6, 11, 16, ...).

Hence the parameters are given as follows:

m = 5, b = 6.

Thus the definition of the function is of:

T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).

T(n) = 5n + 1.

Then the number of hexagons with 61 toothpicks is obtained as follows:

5n + 1 = 61

5n = 60

n = 60/5

n = 12 hexagons.

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Answer:

9

Step-by-step explanation:

In the notation of a function f(x) = x+8, for input x=1 the output would be 9. And (1,9) would be an (x,y) pair that fits the function.

The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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Therefore, the line integral is:

∫c xy^4 ds = 125∫[0,pi] cos(t)sin^4(t) dt = 125(48/5) = 1200

The right half of the circle x^2 + y^2 = 25 can be parameterized as c(t) = (5cos(t), 5sin(t)) for t in [0, pi], where the orientation is counterclockwise.

The line integral of xy^4 along c is given by:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

where ||c'(t)|| is the magnitude of the derivative of c with respect to t.

We have:

c'(t) = (-5sin(t), 5cos(t))

||c'(t)|| = sqrt[(-5sin(t))^2 + (5cos(t))^2] = 5sqrt(sin^2(t) + cos^2(t)) = 5

So the line integral becomes:

∫c xy^4 ds = ∫[0,pi] xy^4 ||c'(t)|| dt

= 5∫[0,pi] 25cos(t)sin^4(t) dt

= 125∫[0,pi] cos(t)sin^4(t) dt

To evaluate this integral, we can use integration by substitution. Let u = sin(t), then du/dt = cos(t) and dt = du/cos(t). So we have:

∫cos(t)sin^4(t) dt = ∫u^4 du/cos(t) = ∫u^4 sec(t) du

We can evaluate this integral as follows:

∫u^4 sec(t) du = sec(t)u^5/5 - 2/5 ∫u^2 sec(t) du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 4/15 ∫u^2 du

= sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3 + C

where C is the constant of integration.

Substituting back u = sin(t) and integrating over [0,pi], we obtain:

∫[0,pi] cos(t)sin^4(t) dt

= [sec(t)u^5/5 - 2/5 tan(t)u^3/3 + 2/5 u^3]_0^pi

= (0 - 0 + 2/5(5^3)) - (1/5 - 0 + 0)

= 48/5

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The company's working capital and current ratio are important financial metrics used to assess its short-term liquidity and financial health. The working capital represents the company's ability to meet its short-term obligations, while the current ratio indicates its ability to cover current liabilities with current assets. To compute the working capital and current ratio, relevant financial information is required, such as current assets and current liabilities.

Working capital is calculated by subtracting current liabilities from current assets. Current assets typically include cash, accounts receivable, and inventory, while current liabilities include accounts payable, short-term debt, and accrued expenses. The formula for working capital is:

Working Capital = Current Assets - Current Liabilities

The working capital figure provides insights into the company's liquidity and its ability to cover short-term obligations. A positive working capital indicates that the company has sufficient current assets to meet its current liabilities, which is generally considered favorable.

The current ratio is another important metric that assesses a company's liquidity. It is calculated by dividing current assets by current liabilities. The formula for the current ratio is:

Current Ratio = Current Assets / Current Liabilities

The current ratio reflects the company's ability to pay off its current liabilities using its current assets. It provides a measure of the company's short-term financial strength and its capacity to handle immediate obligations. A higher current ratio is generally considered more favorable, as it indicates a greater ability to cover short-term liabilities.

In conclusion, by computing the working capital and current ratio, analysts and investors can gain valuable insights into a company's short-term liquidity and financial health. These metrics help assess the company's ability to meet its obligations and manage its current assets and liabilities effectively.

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Answer:

Formula for volume of hemisphere;

V = 2/3 * π * \(r^{3}\)

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * \(r^{3}\)

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.